A multiplexed display is a method to come away with far lesser pins and wires. The principle is turning on only one digit at one time, one after the other - but at a very high frequency, so that they appear to light up all at once.

The animation below shows the principle at a lower "scan frequency":

When the scan frequency goes up to over 15 cycles per second the perception of the human eye can no longer differ between the separate displays but sees all four displayed numbers at one time.

Main advantage in our case: we need 10 cathode lines and 4 anode lines and that was it. Totals 14 wires to the Nixies instead of 41 in the best case for an unmultiplexed display - 4 x 10 cathodes and +Ub - given that the anode resistors are located elsewhere on the Nixie sockets.